text: A standard configuration for a Penning trap consists of a ring electrode and two end caps. A static voltage differential between the ring and end caps confines ions along the axial direction (between end caps). However, as expected from Earnshaw's theorem, the static electric potential is not sufficient to trap an ion in all three dimensions. To provide the radial confinement, a strong axial magnetic field is applied.
  For a uniform electric field , the force  accelerates a positively charged ion along the -axis. For a uniform magnetic field , the Lorentz force causes the ion to move in circular motion with cyclotron frequency
  Assuming an ion with zero initial velocity placed in a region with  and , the equations of motion are
  The resulting motion is a combination of oscillatory motion around the -axis with frequency  and a drift velocity in the -direction. The drift velocity is perpendicular to the direction of the electric field.
  For the radial electric field produced by the electrodes in a Penning trap, the drift velocity will precess around the axial direction with some frequency , called the magnetron frequency. An ion will also have a third characteristic frequency  between the two end cap electrodes. The frequencies usually have widely different values with .